Here is a chart comparing the Balance Sheet Assets of the Fed and the European Central Bank.
It is important to recall that the Fed has been providing extensive funding to non-US, largely European, multinational Banks through their US subsidiaries.
This also does not compare the sovereign debt of the two regions, but rather just one measure of their Central Banks policy responses. It does not indicate how those assets are being used, by whom, and to what effect.
Nevertheless there seems to be a clear divergence between the two policy responses.